Spin-wave resonance frequency in a multi-layer film

The spin-wave resonance (SWR) frequency in a ferromagnetic bilayer or triple-layer film (for bilayer or triple-layer films, including symmetric and asymmetric films) with single-ion anisotropy has been studied by using the linear spin-wave approximation and Green's function technique. The effects of interfacial coupling, surface anisotropy, interface anisotropy, bulk anisotropy and external magnetic field on the SWR frequency have been investigated. For a ferromagnetic bilayer or triple-layer film, the SWR frequencies (for the same spin-wave modes) all increase with increasing external magnetic field, surface anisotropy, interface anisotropy and bulk anisotropy and with decreasing film thickness. As the interfacial coupling increases, the SWR frequencies of some modes increase, while the SWR frequencies of the other modes do not change. The SWR frequencies of a triple-layer film are different from those of a bilayer film and the SWR frequencies of an asymmetric film are also different from those of a symmetric film. The present results show the method to enhance and adjust the SWR frequency of ferromagnetic multi-layer films.